GenPareto_Layer_SM function

Second Layer Moment of the Generalized Pareto Distribution

Calculates the second moment of a generalized Pareto distribution in a reinsurance layer

GenPareto_Layer_SM(
  Cover,
  AttachmentPoint,
  t,
  alpha_ini,
  alpha_tail,
  truncation = NULL
)

Arguments

• Cover: Numeric. Cover of the reinsurance layer. Use Inf for unlimited layers.
• AttachmentPoint: Numeric. Attachment point of the reinsurance layer.
• t: Numeric. Threshold of the Pareto distribution. If t is NULL (default) then t <- Attachment Point is used
• alpha_ini: Numeric. Initial Pareto alpha (at t).
• alpha_tail: Numeric. Tail Pareto alpha.
• truncation: Numeric. If truncation is not NULL and truncation > t, then the Pareto distribution is truncated at truncation.

Returns

The second moment of the (truncated) generalized Pareto distribution with parameters t, alpha_ini and alpha_tail in the layer Cover xs AttachmentPoint

Examples

GenPareto_Layer_SM(4000, 1000, 1000, 1, 2)
GenPareto_Layer_SM(4000, 1000, t = 1000, alpha_ini = 1, alpha_tail = 3)
GenPareto_Layer_SM(4000, 1000, t = 5000, alpha_ini = 1, alpha_tail = 3)
GenPareto_Layer_SM(4000, 1000, t = 1000, alpha_ini = 1, alpha_tail = 3, truncation = 5000)
GenPareto_Layer_SM(9000, 1000, t = 1000, alpha_ini = 1, alpha_tail = 3, truncation = 5000)